SOLUTION: Hi...this would be extremely beneficial for me if somebody could help with this problem: Find the length of each side of a regular hexagon if opposite sides from midpoint to midpo
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Question 80365: Hi...this would be extremely beneficial for me if somebody could help with this problem: Find the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart.
You can put this solution on YOUR website! Find the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart.
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Draw the picture.
Notice that half of the line segment connecting the opposite midpoints
is the perpendicular bisector of a triangle formed by connecting
the center to the two adjoining vertices.
That perpendicular bisector is 9 inches long
The base angles of that triangle are each 60 degrees because the figure
is a regular hexagon. The smaller angle in the little triangle formed
s 30 degrees. So the side opposite is half the hypotenuse.
Let the hypotenuse be 2x; then the smaller side is x.
Use Pythagoras to get:
(2x)^2= x^2 + 9^2
3x^2=81
x^2=27
x=3sqrt3
That is hal the lenth of the side.
So the side is 6sqrt3
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cheers,
stan H.
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